Question

1 use angle relationships to complete the top equation. then, solve the equation for x and find the measure of both angles. x = 180° x = 14x = 4x =

Explanation:

Step1: Identify angle - relationship

The angles \(14x\) and \(4x\) are supplementary (they form a straight - line), so \(14x + 4x=180^{\circ}\).

Step2: Combine like - terms

\(18x = 180^{\circ}\)

Step3: Solve for \(x\)

Divide both sides by 18: \(x=\frac{180^{\circ}}{18}=10^{\circ}\)

Step4: Find the measure of \(14x\)

Substitute \(x = 10^{\circ}\) into \(14x\), we get \(14\times10^{\circ}=140^{\circ}\)

Step5: Find the measure of \(4x\)

Substitute \(x = 10^{\circ}\) into \(4x\), we get \(4\times10^{\circ}=40^{\circ}\)

Answer:

The completed equation is \(14x + 4x=180^{\circ}\), \(x = 10^{\circ}\), \(14x = 140^{\circ}\), \(4x = 40^{\circ}\)